The defender had an opportunity to draw the Foxes level at the death but his header flew just wide, allowing the visitors to run away with a 2-1 win at King Power Stadium.
He started the match at right-back before moving to central defence following the sending off of captain Wes Morgan in the 63rd minute.
“We’re disappointed of course, we didn’t start the game with enough tempo, it’s another time we conceded a goal after six minutes," Puel said, as reported by his club's official website.
“At the end, we had the last chance – 10 men against 11 after a good corner for us.
“With Daniel, we [could have] come back into the game and scored. It was a good opportunity for the squad because they worked a lot.
"It was a tough game, a good opponent and it’s a shame. We have a lot of disappointment.”
Leicester's first defeat in four games in all competitions, the result has left the club on the 10th position on the league table, one place above Everton.
Amartey has made seven league appearances involving five starts so far for the Foxes this season.
He has been called up for Ghana's 2019 Africa Cup of Nations qualifying double-header against Sierra Leone on October 11 and 15.